1 thought on “In variation of parameters method,<br />the Wronskian W is given by”
Answer:
thanks
Step-by-step explanation:
In the last section we looked at the method of undetermined coefficients for finding a particular solution to
p
(
t
)
y
′′
+
q
(
t
)
y
′
+
r
(
t
)
y
=
g
(
t
)
(1)
and we saw that while it reduced things down to just an algebra problem, the algebra could become quite messy. On top of that undetermined coefficients will only work for a fairly small class of functions.
The method of Variation of Parameters is a much more general method that can be used in many more cases. However, there are two disadvantages to the method. First, the complementary solution is absolutely required to do the problem. This is in contrast to the method of undetermined coefficients where it was advisable to have the complementary solution on hand but was not required. Second, as we will see, in order to complete the method we will be doing a couple of integrals and there is no guarantee that we will be able to do the integrals. So, while it will always be possible to write down a formula to get the particular solution, we may not be able to actually find it if the integrals are too difficult or if we are unable to find the complementary solution.
We’re going to derive the formula for variation of parameters. We’ll start off by acknowledging that the complementary solution to
Answer:
thanks
Step-by-step explanation:
In the last section we looked at the method of undetermined coefficients for finding a particular solution to
p
(
t
)
y
′′
+
q
(
t
)
y
′
+
r
(
t
)
y
=
g
(
t
)
(1)
and we saw that while it reduced things down to just an algebra problem, the algebra could become quite messy. On top of that undetermined coefficients will only work for a fairly small class of functions.
The method of Variation of Parameters is a much more general method that can be used in many more cases. However, there are two disadvantages to the method. First, the complementary solution is absolutely required to do the problem. This is in contrast to the method of undetermined coefficients where it was advisable to have the complementary solution on hand but was not required. Second, as we will see, in order to complete the method we will be doing a couple of integrals and there is no guarantee that we will be able to do the integrals. So, while it will always be possible to write down a formula to get the particular solution, we may not be able to actually find it if the integrals are too difficult or if we are unable to find the complementary solution.
We’re going to derive the formula for variation of parameters. We’ll start off by acknowledging that the complementary solution to
(1)
is